Question

g 3. an annuity is 20 payments of $200 paid semiannually. interest is 12% compounded semiannually. find the value:

Answer 1

The value of the annuity is approximately $12,171.40.

How to solve

To find the total value of an annuity comprising 20 semiannual payments of $200, with an interest rate of 12% compounded semiannually, the formula for the present value of an annuity is used:

This formula computes the current worth of future cash flows considering interest rates.

`PV = PMT * (1 - (1 + r/n)^(-nt)) / r/n`

Where:

PV: Present value of the annuity

PMT: Periodic payment amount ($200)

r: Annual interest rate (12%)

n: Number of compounding periods per year (2)

t: Total number of years (20/2 = 10)

Plugging in the values:

PV =
`200 * (1 - (1 + 0.12/2)^(-20)) / 0.12/2`

PV ≈ $12,171.40

Therefore, the value of the annuity is approximately $12,171.40.